Lack-of-Fit Testing of a Regression Model with Response Missing at Random

• Activity Number: 630
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Xiaoyu Li*+
• Companies: Michigan State University
• Keywords: kernel estimator ; consistency ; local alternative ; missing at random

Abstract

This paper proposes a class of lack-of-fit tests for fitting a linear regression model when some response variables are missing at random. These tests are based on a class of minimum integrated square distances between a kernel type estimator of a regression function and the parametric regression function being fitted, where the former is constructed by imputation method. These tests are shown to be consistent against a large class of fixed alternatives. The corresponding test statistics are shown to have asymptotic normal distributions under null hypothesis and a class of nonparametric local alternatives. Two simulation studies are reported. The first simulation study describes the finite sample behavior of the empirical size and power of the test at four alternatives under different designs and data missing mechanisms. The second simulation reports the finite sample behavior of the minimum distance estimator of the null parameter.